U.S. patent application number 13/718387 was filed with the patent office on 2014-06-19 for control system and method for mitigating loads during yaw error on a wind turbine.
This patent application is currently assigned to GENERAL ELECTRIC COMPANY. The applicant listed for this patent is GENERAL ELECTRIC COMPANY. Invention is credited to Rajeeva Kumar, Charudatta Subhash Mehendale.
Application Number | 20140169964 13/718387 |
Document ID | / |
Family ID | 49766921 |
Filed Date | 2014-06-19 |
United States Patent
Application |
20140169964 |
Kind Code |
A1 |
Kumar; Rajeeva ; et
al. |
June 19, 2014 |
CONTROL SYSTEM AND METHOD FOR MITIGATING LOADS DURING YAW ERROR ON
A WIND TURBINE
Abstract
A control system for mitigating loads on a wind turbine
comprising a plurality of blades in yaw error events includes a yaw
error calculation unit for calculating a yaw error of the wind
turbine, a pitch angle reference command calculation unit for
calculating a plurality of pitch angle reference commands
respectively corresponding to the plurality of blades at least
based on the calculated yaw error, and a controller for producing a
plurality of pitch commands at least based on the plurality of
pitch angle reference commands, to respectively regulate the pitch
angles of the plurality of blades.
Inventors: |
Kumar; Rajeeva; (Clifton
Park, NY) ; Mehendale; Charudatta Subhash;
(Niskayuna, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
GENERAL ELECTRIC COMPANY |
Schenectady |
NY |
US |
|
|
Assignee: |
GENERAL ELECTRIC COMPANY
Schenectady
NY
|
Family ID: |
49766921 |
Appl. No.: |
13/718387 |
Filed: |
December 18, 2012 |
Current U.S.
Class: |
416/1 ;
416/147 |
Current CPC
Class: |
Y02E 10/723 20130101;
F05B 2270/329 20130101; F03D 7/0224 20130101; F03D 7/0204 20130101;
Y02E 10/72 20130101 |
Class at
Publication: |
416/1 ;
416/147 |
International
Class: |
F03D 7/02 20060101
F03D007/02 |
Claims
1. A control system for mitigating loads on a wind turbine
comprising a plurality of blades in yaw error events, the control
system comprising: a yaw error calculation unit for calculating a
yaw error of the wind turbine; a pitch angle reference command
calculation unit for calculating a plurality of pitch angle
reference commands respectively corresponding to the plurality of
blades at least based on the calculated yaw error; and a controller
for producing a plurality of pitch commands at least based on the
plurality of pitch angle reference commands, to respectively
regulate the pitch angles of the plurality of blades.
2. The control system of claim 1, further comprising: a rotor speed
command setting unit for calculating a rotor speed reference
command at least based on the calculated yaw error; and a
controller for producing a rotor speed command, to regulate the
rotor speed of the wind turbine at least based on the rotor speed
reference command.
3. The control system of claim 1, further comprising: a power
command setting unit for calculating a power reference command at
least based on the calculated yaw error; and a controller for
producing a power command, to regulate the power of the wind
turbine at least based on the power reference command.
4. The control system of claim 1, wherein the pitch angle reference
command calculation unit comprises: a plurality of mean inflow
angle calculation units for calculating a plurality of respective
mean inflow angles corresponding to the plurality of blades; and a
reference angle of attack calculation unit for calculating a
plurality of respective reference angles of attack corresponding to
the plurality of blades based on the calculated yaw error and a
predefined load limit; wherein the plurality of pitch angle
reference commands are calculated by calculating the difference
between the plurality of mean inflow angles and the plurality of
reference angles of attack.
5. The control system of claim 4, wherein each of the plurality of
mean inflow angle calculation units calculates the corresponding
mean inflow angle based on one or more parameter signals from the
corresponding blade.
6. The control system of claim 5, wherein the one or more parameter
signals comprise wind speed, wind direction, blade azimuth angle,
and rotor speed.
7. The control system of claim 6, wherein an inflow angle is
calculated based on the equation: .PHI. ( r ) = tan - 1 V cos
.beta. V sin .beta. cos .lamda. + r .OMEGA. ; ##EQU00002## wherein
.phi.(r) is the inflow angle on the corresponding blade as a
function of a blade span location r of the corresponding blade, V
stands for a wind speed, .OMEGA. stands for a rotor speed, .beta.
stands for a wind direction in inertial reference frame, .lamda.
stands for a blade azimuth angle.
8. The control system of claim 7, wherein the plurality of pitch
angle reference commands .theta. are calculated based on the
equation: .alpha..sub.m=mean(.phi.(r))-.theta.; wherein
.alpha..sub.m stands for the reference angle of attack,
mean(.phi.(r)) is a mean value of the inflow angle .phi.(r).
9. The control system of claim 8, wherein the mean value of the
inflow angle .phi.(r) is calculated as the mathematical average
value of inflow angles obtained over 60%-90% of that blade span of
the corresponding blade.
10. The control system of claim 1, wherein the yaw error
calculation unit further provides a shutdown command to shut the
wind turbine down when the calculated yaw error is greater than a
predetermined maximum allowable yaw error.
11. The control system of claim 1, wherein the pitch angle
reference command calculation unit comprises: a plurality of mean
AoA calculation units for calculating a plurality of respective
mean angles of attack corresponding to the plurality of blades; an
AoA limit unit for setting an AoA limitation value based on the
calculated yaw error or a predetermined yaw error condition; and a
plurality of block elements for blocking the plurality of mean
angles of attack when the plurality of mean angles of attack are
equal to or less than the AoA limitation value; wherein the
plurality of pitch angle reference commands are calculated by
calculating the summation of the plurality of mean angles of attack
and a plurality of pitch angle feedback signals.
12. The control system of claim 1, further comprising an individual
blade pitch control unit for producing a plurality of pitch angle
compensation commands to respectively compensate the plurality of
pitch commands, wherein the plurality of pitch angle compensation
commands are calculated by calculating the difference between a
plurality of respective mean angles of attack or inflow angles of
the plurality of blades and the corresponding average value.
13. The control system of claim 12, wherein the individual blade
pitch control unit comprises: a plurality of mean AoA calculation
units for calculating a plurality of respective mean angles of
attack corresponding to the plurality of blades; and an average AoA
calculation unit for calculating an average value of the calculated
plurality of respective mean angles of attack; wherein the
plurality of pitch angle compensation commands are calculated by
calculating the difference between the plurality of respective mean
angles of attack and the average value.
14. The control system of claim 12, wherein the individual blade
pitch control unit comprises: a plurality of mean inflow angle
calculation units for calculating a plurality of respective mean
inflow angles corresponding to the plurality of blades; and an
average inflow angle calculation unit for calculating an average
value of the calculated plurality of respective mean inflow angles;
wherein the plurality of pitch angle compensation commands are
calculated by calculating the difference between the plurality of
respective mean inflow angles and the average value.
15. A control method for mitigating loads on a wind turbine
comprising a plurality of blades in yaw error events, the control
method comprising: calculating a yaw error of the wind turbine;
calculating a plurality of pitch angle reference commands
respectively corresponding to the plurality of blades at least
based on the calculated yaw error; and producing a plurality of
pitch commands at least based on the plurality of pitch angle
reference commands, to respectively regulate the pitch angles of
the plurality of blades.
16. The control method of claim 15, wherein calculating a plurality
of pitch angle reference commands respectively corresponding to the
plurality of blades at least based on the calculated yaw error
comprises: calculating a plurality of respective mean inflow angles
corresponding to the plurality of blades; calculating a plurality
of respective reference angles of attack corresponding to the
plurality of blades based on the calculated yaw error and a
predefined load limit; and calculating the plurality of pitch angle
reference commands by calculating the difference between the
plurality of mean inflow angles and the plurality of reference
angles of attack.
17. The control method of claim 15, wherein calculating a plurality
of pitch angle reference commands respectively corresponding to the
plurality of blades at least based on the calculated yaw error
comprises: calculating a plurality of respective mean angles of
attack corresponding to the plurality of blades; setting an AoA
limitation value based on the calculated yaw error or a predefined
yaw error; blocking the plurality of mean angles of attack when the
plurality of mean angles of attack are equal to or less than the
AoA limitation value; and calculating the plurality of pitch angle
reference commands by calculating the summation of the plurality of
mean angles of attack and a plurality of pitch angle feedback
signals.
18. The control method of claim 15, further comprising producing a
plurality of pitch angle compensation commands to respectively
compensate the plurality of pitch commands, wherein the plurality
of pitch angle compensation commands are calculated by calculating
the difference between a plurality of respective mean angles of
attack or inflow angles of the plurality of blades and the
corresponding average value.
19. The control method of claim 18, wherein producing a plurality
of pitch angle compensation commands to respectively compensate the
plurality of pitch commands comprises: calculating a plurality of
respective mean angles of attack corresponding to the plurality of
blades; calculating an average value of the calculated plurality of
respective mean angles of attack; and calculating the plurality of
pitch angle compensation commands by calculating the difference
between the plurality of respective mean angles of attack and the
average value.
20. The control method of claim 18, wherein producing a plurality
of pitch angle compensation commands to respectively compensate the
plurality of pitch commands comprises: calculating a plurality of
respective mean inflow angles corresponding to the plurality of
blades; calculating an average value of the calculated plurality of
respective mean inflow angles; and calculating the plurality of
pitch angle compensation commands by calculating the difference
between the plurality of respective mean inflow angles and the
average value.
21. A control system for mitigating loads on a wind turbine
comprising a plurality of blades in yaw error events, the control
system comprising: a controller for producing a plurality of pitch
commands, to respectively regulate the pitch angles of the
plurality of blades; and an individual blade pitch control unit for
producing a plurality of pitch angle compensation commands to
respectively compensate the plurality of pitch commands; wherein
the plurality of pitch angle compensation commands are calculated
by calculating the difference between a plurality of respective
mean angles of attack or inflow angles of the plurality of blades
and the corresponding average value.
22. The control system of claim 21, wherein the individual blade
pitch control unit comprises: a plurality of mean AoA calculation
units for calculating a plurality of respective mean angles of
attack corresponding to the plurality of blades; and an average AoA
calculation unit for calculating an average value of the calculated
plurality of respective mean angles of attack; wherein the
plurality of pitch angle compensation commands are calculated by
calculating the difference between the plurality of respective mean
angles of attack and the average value.
23. The control system of claim 21, wherein the individual blade
pitch control unit comprises: a plurality of mean inflow angle
calculation units for calculating a plurality of respective mean
inflow angles corresponding to the plurality of blades; and an
average inflow angle calculation unit for calculating an average
value of the calculated plurality of respective mean inflow angles;
wherein the plurality of pitch angle compensation commands are
calculated by calculating the difference between the plurality of
respective mean inflow angles and the average value.
24. The control system of claim 21, further comprising: a rotor
speed command setting unit for calculating a rotor speed reference
command at least based on a calculated yaw error; and a controller
for producing a rotor speed command, to regulate the rotor speed of
the wind turbine at least based on the rotor speed reference
command.
25. The control system of claim 21, further comprising: a power
command setting unit for calculating a power reference command at
least based on a calculated yaw error; and a controller for
producing a power command, to regulate the power of the wind
turbine at least based on the power reference command.
Description
BACKGROUND
[0001] Embodiments of the disclosure relate generally to wind
turbines and, more particularly, for mitigating loads during yaw
error conditions experienced by wind turbines.
[0002] A utility-scale wind turbine typically includes a set of two
or three large rotor blades mounted to a hub. The rotor blades and
the hub together are referred to as a rotor. The rotor blades
aerodynamically interact with the wind and create lift and drag,
which is then translated into a driving torque by the rotor. The
rotor is attached to and drives a main shaft, which in turn is
operatively connected via a drive train to a generator or a set of
generators that produce electric power. The main shaft, the drive
train and the generator(s) are all situated within a nacelle, which
rests on a yaw system that continuously pivots along a vertical
axis to keep the rotor blades facing in the direction of the
prevailing wind current to generate maximum torque.
[0003] In certain circumstances, the wind direction can shift
faster than the response of the yaw system, which can result in a
yaw error. Yaw error is typically defined as the difference (e.g.,
angular difference) between the orientation of the wind turbine
nacelle and the wind direction and occurs when the wind turbine
nacelle is not aligned with the wind. During such aforementioned
transient wind events, the yaw error, which can be sustained for a
few seconds or minutes (until the yaw system points the wind
turbine nacelle to face the wind), might damage the wind turbine if
operation of the wind turbine continues. Specifically, during such
operation of the wind turbine, yaw error can result in unacceptably
high loads on the rotor blades, hub, tower, and other components
thereof, which can result in damage.
[0004] Yaw error can be avoided by actively adjusting the
orientation of the wind turbine nacelle with the yaw system, i.e.
by keeping the wind turbine nacelle pointed directly into the wind.
However, as mentioned above, the wind direction may shift quite
rapidly and faster than the response of the yaw system. A technique
proposed in the past handles extreme yaw error by simply shutting
down the wind turbine in those extreme yaw error conditions and
then restarting once the wind turbine nacelle is properly oriented
into the wind. When the wind turbine shut down is initiated, it
goes through a shut down cycle and then a startup cycle, which
results in several minutes of lost energy production. In addition,
high mechanical loading can occur on turbine components if the
shutdown procedure is not tailored to an extreme yaw error
condition.
[0005] Therefore, there is a need for new and improved control
systems and methods for mitigating loads during extreme yaw error
on a wind turbine.
BRIEF DESCRIPTION
[0006] A control system for mitigating loads during yaw error on a
wind turbine is provided in accordance with one embodiment of the
invention. The control system includes a yaw error calculation unit
for calculating a yaw error of the wind turbine; a pitch angle
reference command calculation unit for calculating a plurality of
pitch angle reference commands respectively corresponding to a
plurality of wind turbine blades at least based on the calculated
yaw error; and a controller for producing a plurality of pitch
commands at least based on the plurality of pitch angle reference
commands, to respectively regulate the pitch angles of the
plurality of blades.
[0007] A control method for mitigating loads during yaw error on a
wind turbine is provided in accordance with one embodiment of the
invention. The control method includes calculating a yaw error of
the wind turbine; calculating a plurality of pitch angle reference
commands respectively corresponding to a plurality of wind turbine
blades at least based on the calculated yaw error; and producing a
plurality of pitch commands at least based on the plurality of
pitch angle reference commands, to respectively regulate the pitch
angles of the plurality of blades.
[0008] A control system for mitigating loads on a wind turbine
including a plurality of blades comprises: a controller for
producing a plurality of pitch commands, to respectively regulate
the pitch angles of the plurality of blades; and an individual
blade pitch control unit for producing a plurality of pitch angle
compensation commands to respectively compensate the plurality of
pitch commands; wherein the plurality of pitch angle compensation
commands are calculated by calculating the difference between a
plurality of respective mean angles of attack or inflow angles of
the plurality of blades and the corresponding average value.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] These and other features, aspects, and advantages of the
present disclosure will become better understood when the following
detailed description is read with reference to the accompanying
drawings in which like characters represent like parts throughout
the drawings, wherein:
[0010] FIG. 1 is a schematic diagram of a wind turbine.
[0011] FIG. 2 is a schematic block diagram of a control system of a
wind turbine, in accordance with at least some embodiments of the
present disclosure.
[0012] FIG. 3 is a schematic diagram of an example blade of the
wind turbine of FIG. 1, together showing some parameters of the
blade.
[0013] FIG. 4 is a schematic diagram of a control block for
mitigating loads during yaw error on a wind turbine, in accordance
with one embodiment of the present disclosure.
[0014] FIG. 5 is a flowchart of a control method for mitigating
loads during yaw error on a wind turbine, in accordance with at
least some embodiments of the present disclosure.
[0015] FIG. 6 is a comparison diagram of a simulation of a trend of
pitch angles of three blades when not controlled by the control
method of FIG. 5 and a trend of pitch angles of three blades when
controlled by the control method of FIG. 5.
[0016] FIG. 7 is a comparison diagram of a simulation of a trend of
a resultant load of a wind turbine not controlled by the control
method of FIG. 5 and a trend of a resultant load of a wind turbine
controlled by the control method of FIG. 5 while maintaining the
rotor speed the same as in the conventional control method.
[0017] FIG. 8 is a schematic diagram of a control block for further
providing rotor speed and power setting control during yaw error on
a wind turbine, in accordance with at least some embodiments of the
present disclosure.
[0018] FIG. 9 is a schematic diagram of a control block for
mitigating loads during yaw error on a wind turbine, in accordance
with another embodiment of the present disclosure.
[0019] FIG. 10 is a partial schematic block diagram of a control
system for mitigating loads during yaw error on a wind turbine, in
accordance with at least some embodiments of the present
disclosure.
[0020] FIG. 11 is a schematic diagram of an individual blade pitch
control unit of the control system of FIG. 10, in accordance with
one embodiment of the present disclosure.
[0021] FIG. 12 is a schematic diagram of an individual blade pitch
control unit of the control system of FIG. 10, in accordance with
another embodiment of the present disclosure.
DETAILED DESCRIPTION OF THE DISCLOSURE
[0022] One or more specific embodiments of the present disclosure
will be described below. In an effort to provide a concise
description of these embodiments, not all features of an actual
implementation are described in the specification. It should be
appreciated that in the development of any such actual
implementation, as in any engineering or design project, numerous
implementation-specific decisions must be made to achieve the
developers' specific goals, such as compliance with system-related
and business-related constraints, which may vary from one
implementation to another. Moreover, it should be appreciated that
such a development effort might be complex and time consuming, but
would nevertheless be a routine undertaking of design, fabrication,
and manufacture for those of ordinary skill having the benefit of
this disclosure.
[0023] Unless defined otherwise, technical and scientific terms
used herein have the same meaning as is commonly understood by one
of ordinary skill in the art to which this disclosure belongs. The
terms "first", "second", and the like, as used herein do not denote
any order, quantity, or importance, but rather are used to
distinguish one element from another. Also, the terms "a" and "an"
do not denote a limitation of quantity, but rather denote the
presence of at least one of the referenced items. The term "or" is
meant to be inclusive and mean either or all of the listed items.
The use of "including," "comprising" or "having" and variations
thereof herein are meant to encompass the items listed thereafter
and equivalents thereof as well as additional items.
[0024] Referring to FIG. 1, an exemplary wind turbine 10 is shown.
While all the components of the wind turbine 10 have not been shown
and/or described, a typical wind turbine 10 may include a tower 12
and a rotor 14. The rotor 14 may include a plurality of blades (for
example three blades 141, 142, and 143) connected to a hub 144. The
blades 141-143 may rotate with wind energy and the rotor 14 may
transfer that energy to a main shaft (not shown) situated within a
nacelle 16. The nacelle 16 may optionally include a drive train
(not shown), which may connect the main shaft on one end to one or
more generators (not shown) on the other end. Alternatively, the
generator(s) may be connected directly to the main shaft in a
direct drive configuration. The generator(s) may generate power,
which may be transmitted through the tower 12 to a power
distribution panel (PDP) and a pad mount transformer (PMT) for
transmission to a grid (not shown). The nacelle 16 may be
positioned on a yaw system, which may pivot about a vertical axis
to orient the nacelle 16 in the direction of the wind current.
[0025] In addition to the aforementioned components, the wind
turbine 10 may also include a control system 20 (FIG. 2) may be
situated within the nacelle 16 for controlling the various
components of the wind turbine 10, for example controlling the
pitch (e.g., angle of blades with respect to the wind direction) of
the blades 141-143, controlling the rotor speed, controlling the
power, controlling the torque, etc. The wind turbine 10 may also
include multiple sensors (not shown) mounted on different positions
of the wind turbine 10 to sense/measure multiple parameters, such
as power, rotor speeds, vibrations, deflections, load, wind speed,
wind direction, wind shear/veer, etc. The following paragraphs and
figures will mainly describe the pitch control part of the control
system 10 in detail, which is used to solve the yaw error problem.
The other control parts of the control system 10 may use
conventional strategies which are not described in detail, or may
be changed according to the pitch control part and will be
described as well. Furthermore, FIG. 1 only shows an exemplary wind
turbine 10 to explain a general working process for a general wind
turbine. In other embodiments, the wind turbine 10 may comprise a
different type of wind turbine.
[0026] Referring to FIG. 2, an exemplary control system 20 of the
wind turbine 10 is shown, in accordance with at least some
embodiments of the present disclosure. While all the components of
the control system 20 have not been shown and/or described, a
typical control system 20 may include a scheduler 22, an estimator
24, and a controller 26. FIG. 2 only shows an exemplary control
system 20 to explain a general controlling process for a general
wind turbine 10. In other embodiments, the control system 20 may
comprise other components or just comprise one control unit which
integrates all functions therein.
[0027] In general, the scheduler 22 is used to receive some
external commands and sensed signals/feedback signals, and then
calculate corresponding reference commands based on the received
reference commands and sensed signals/feedback signals, for
providing control reference commands to the controller 26. For
example, the external commands may include reference angle of
attack (AoA) commands, power curtailment commands, ramp rate
control commands, noise reduced operation commands, which may be
generated from a wind farm management system (not shown). The
sensed signals/feedback signals may include power, rotor speed,
vibrations, deflections, loads, wind speed, wind shear/veer
signals, etc., sensed by the sensors or read directly from a
controller memory (not shown). These reference commands may include
power reference commands, rotor speed reference commands, pitch
angle reference commands, generator torque reference commands,
control mode reference commands, etc. The following paragraphs and
figures will describe some exemplary embodiments of the pitch
control part (FIGS. 4 and 9), the power control part and the rotor
speed control part (FIG. 8) of the scheduler 22 in detail.
[0028] In general, the estimator 24 is used to receive sensed
signals and feedback signals, and then estimate/calculate some
parameters that are not directly measured. The feedback signals may
include current values of pitch and torque feedback signals. The
feedback signals may be sensed or read directly from a controller
memory (not shown). The estimated parameters may include average
wind speed, tower and blade velocities, etc. It is understood that
the estimator 24 can use appropriate algorithms to estimate these
parameters, which are well-known technology and thus not described
in detail.
[0029] In general, the controller 26 is used to receive the
reference commands from the scheduler 22, the estimated parameters
from the estimator 24, and the sensed signals from the sensors, and
then calculate corresponding control commands to control the wind
turbine 10 based on those received commands, parameters, and
signals. The control commands may include pitch commands, generator
torque commands, yaw angle or rate commands etc. In some
embodiments, the controller 26 may use any appropriate conventional
algorithm to achieve such control commands. In some other
embodiments, an individual blade pitch control unit 28 (see FIGS.
10, 11, and 12) is used to cooperate with the controller 26 to
generate compensated pitch commands for further mitigating loads
during yaw error on the wind turbine 10. In other embodiments,
other functions of additional control units may be introduced to
cooperate with the controller 26 to implement different functions
for controlling the wind turbine 10 according to other
requirements.
[0030] Referring to FIG. 3, a schematic diagram of an example blade
142 of the wind turbine 10 of FIG. 1 is shown. Here, r stands for a
blade span location, .phi. stands for an inflow angle, a stands for
an angle of attack (AoA), V stands for a wind speed (velocity),
V.sub.r stands for a resultant relative wind speed at the radius r,
.OMEGA. stands for a rotational velocity of the blade 142. It is
understood that the resultant relative wind speed V.sub.r has
contributions from the wind speed V and the rotational velocity
.OMEGA.. When ignoring the 3-dimensional flow effect, the inflow
angle .phi. at the blade span location r is approximated as:
.PHI. ( r ) = tan - 1 V cos .beta. V sin .beta.cos .lamda. + r
.OMEGA. Eq . 1 ##EQU00001##
In other embodiments, a more detailed expression for inflow angle
may further include other parameters, such as wind shear, wind
upflow angle, shaft tilt, blade pre-cone angle, blade structural
twist angle, tower bending, etc. A mean value of the angle of
attack (AoA) .alpha..sub.m is defined as:
.alpha..sub.m=mean(.phi.(r))-.theta. Eq. 2
Where .phi.(r) is the inflow angle .phi. on the blade 142 as a
function of the blade span location r, mean(.phi.(r)) is a mean
value of .phi.(r), .OMEGA. stands for the rotor speed, .beta.
stands for a wind direction in inertial reference frame, .lamda.
stands for a blade azimuth angle, .theta. stands for a blade pitch
angle.
[0031] The above equations Eq. 1 and Eq. 2 are general equations
used to calculate the mean value of angle of attack .alpha..sub.m.
On a blade 142, the produced load (force) is dominated by
aerodynamic loads, and these aerodynamic loads depend on
distribution of AoA along the blade span, which may be approximated
by the mean value of the angle of attack .alpha..sub.m at certain
span locations at the corresponding blade 142. Therefore, if there
is a need to reduce the produced load, reducing the angle of attack
.alpha. at a blade 142 can reduce the produced load produced on the
corresponding blade 142 correspondingly. Since most of aerodynamic
loads are produced by span location of the blade 142 far away from
the root section, a mean angle of attack .alpha..sub.m can be
determined through averaging the inflow angle .phi. over span as in
the equation Eq1 and using the equation Eq2. In at least some
embodiments, the mean value for the inflow angle .phi.(r) for each
blade 141, 142, or 143 is calculated as the mathematical average
value of inflow angles obtained over 60%-90% of that blade span of
the corresponding blade 141, 142, or 143, for example over 75% of
that. Furthermore, the angle of attack .alpha. can be modified by
the blade pitch angle .theta., thus the blade pitch angle .theta.
can be controlled to reduce the angle of attack .alpha.. In other
embodiments, depending upon different conditions, such as the
location of the wind turbine 10, the height and size of the tower
12 and the rotor 14 for example, the calculating range of the mean
value for the inflow angle .phi.(r) (namely for the angle of attack
.alpha.) may vary accordingly. In other embodiments, the inflow
angle .phi. of each individual blade 141, 142, or 143 may be
determined by other equations, or directly determined by sensors,
or determined by other methods. In some embodiments, the mean value
for the inflow angle .phi.(r) over certain blade sections also
includes inflow angle values at a single location.
[0032] Referring to FIG. 4 and FIG. 5 together, FIG. 4 shows a
schematic diagram of a control block 40 of the scheduler 22, for
mitigating loads during yaw error on the wind turbine 10, and FIG.
5 shows a flowchart of a control method 50 for mitigating loads
during yaw error on the wind turbine 10 corresponding to the
control block 40, in accordance with one embodiment of the present
disclosure. In FIG. 4, the control block 40 only shows a pitch
control part in the scheduler 22, which is used to provide pitch
angle reference commands (.theta.1_cmd, .theta.2_cmd, .theta.3_cmd)
to the controller 26 for every blade 141, 142, 143, and the other
control parts in the scheduler 22 are not shown in FIG. 4. As an
example, the number of the blades 141, 142, 143 is three, V1, V2
and V3 are first to third wind speeds respectively corresponding to
first to third blades 141, 142, and 143; .beta.1, .beta.2, and
.beta.3 are first to third wind directions in inertial reference
frame respectively corresponding to the first to third blades 141,
142, and 143; .lamda.1, .lamda.2, and .lamda.3 are first to third
blade azimuth angles respectively corresponding to the first to
third blades 141, 142, and 143; and .OMEGA. is the rotor speed. In
some embodiments, these above parameter signals may be
pre-processed in advance, for example by averaging over time, such
as in a 5-10 second moving average window, to smooth these
parameter signals. In some embodiments, the first to third wind
speeds V1, V2, V3 may be equal, the first to third wind directions
.beta.1, .beta.2, and .beta.3 may be equal.
[0033] In step 51, as shown in FIG. 5, parameters, such as yaw
error, which may affect the response of the wind turbine 10 (in
mitigating loads) may be calculated/computed. Specifically, the yaw
error in particular may be described as the angular difference
between the orientation of the wind turbine 10 generally or the
horizontal rotational axis of the rotor 14 more specifically, and
the actual direction of the wind. The yaw error is calculated by a
yaw error calculation unit 49 which may comprise for example, a
sonic anemometer, a wind vane, or a forward looking remote sensing
device.
[0034] In step 52, in at least some embodiments, it may be
determined whether the calculated yaw error is greater than a
predetermined maximum allowable yaw error Ymax. Depending upon the
location of the wind turbine 10, height and size of the tower 12
and the rotor 14 and other related conditions such as wind speed
etc., the predetermined maximum allowable yaw error Ymax may vary.
If the calculated yaw error is greater than the predetermined
maximum allowable yaw error Ymax, the yaw error calculation unit 49
outputs a shutdown command S_cmd to shut the wind turbine 10 down
to avoid damaging the wind turbine 10 (step 58). If the calculated
yaw error is not greater than the predetermined maximum allowable
yaw error Ymax, the process proceeds to the step 53. In other
embodiments, the shutdown control condition may vary based on
different shutdown conditions.
[0035] In step 53, the control block 40 receives parameter signals
from each blade 141, 142, 143. In at least some embodiments, the
control block 40 includes a first mean inflow angle calculation
unit 41, a second mean inflow angle calculation unit 42, and a
third mean inflow angle calculation unit 43. The first mean inflow
angle calculation unit 41 is used to receive parameter signals of
the first wind speed V1, the first wind direction .beta.1, the
first blade azimuth angle .lamda.1, and the rotor speed .OMEGA. of
the first blade 141. The second mean inflow angle calculation unit
42 is used to receive parameter signals of the second wind speed
V2, the second wind direction .beta.2, the second blade azimuth
angle .lamda.2, and the rotor speed .OMEGA. of the second blade
142. The third mean inflow angle calculation unit 43 is used to
receive parameter signals of the third wind speed V3, the third
wind direction .beta.3, the third blade azimuth angle .lamda.3, and
the rotor speed .OMEGA. of the third blade 143. These parameter
signals V1-V3, .lamda.1-.lamda.3, .OMEGA. may be determined by
various sensors (not shown) provided within the wind turbine 10, or
determined by other methods. The first to third wind directions
.beta.1-.beta.3 may be determined based on the calculated yaw error
according to appropriate algorithms or may be determined by other
methods. In some embodiments, the first to third wind speeds V1-V
may be equal, the first to third wind direction .beta.1-.beta.3 may
be equal, under some conditions.
[0036] In step 54, the first mean inflow angle calculation unit 41
is also used to calculate a first mean inflow angle .phi.1 of the
first blade 141 according to above received parameter signals V1,
.beta.1, .lamda.1, .OMEGA., the above equation Eq. 1, and a
predetermined mean range. The second mean inflow angle calculation
unit 42 is used to calculate a second mean inflow angle .phi.2 of
the second blade 142 according to above received parameter signals
V2, .beta.2, .lamda.2, .OMEGA., the above equation Eq. 1, and a
predetermined mean range. The third mean inflow angle calculation
unit 43 is used to calculate a third mean inflow angle .phi.3 of
the third blade 143 according to above received parameter signals
V3, .beta.3, .lamda.3, .OMEGA., the above equation Eq. 1, and a
predetermined mean range. In at least some embodiments, the mean
value of the inflow angle (.phi.1, .phi.2, .phi.3) is calculated as
the mathematical average value of inflow angles obtained over
60%-90% of that blade span of the corresponding blade 141, 142,
143. In other embodiments, the mean inflow angle of each blade may
be determined according to other parameter signals and other
mathematical equations based on aerodynamic principles. If the mean
value is calculated as inflow angle values at a single location,
the predetermined mean range can be omitted.
[0037] In step 55, first to third reference angle of attack
.alpha.1_ref, .alpha.2_ref, .alpha.3_ref are calculated based on
the calculated yaw error of the wind turbine 10 and a predefined
load limit. The first to third reference angle of attack
.alpha.1_ref, .alpha.2_ref, .alpha.3_ref are determined to make
sure each asymmetric load on the first to third blades 141, 142,
and 143 falls within safe range respectively, based on the
predefined load limit. In at least some embodiments, the first to
third reference angle of attack .alpha.1_ref, .alpha.2_ref,
.alpha.3_ref may be calculated through simulation software, such as
Flex5 simulation software or the like. It is understood that these
simulation software tools can dynamically simulate the real working
status of the wind turbine 10 to calculate angle of attack under
different yaw error conditions. In other embodiments, the first to
third reference angle of attack .alpha.1_ref, .alpha.2_ref,
.alpha.3_ref may be calculated by other methods, such as
predetermined equations based on the yaw error for example, and the
first to third reference angle of attack .alpha.1_ref,
.alpha.2_ref, .alpha.3_ref may be equal in some conditions. As
shown in FIG. 4, the control block 40 may include a reference angle
of attack calculation unit 48 to calculate the reference angle of
attack .alpha.1_ref, .alpha.2_ref, .alpha.3_ref based on the step
55 mentioned above.
[0038] In step 56, first to third pitch angle reference commands
.theta.1_cmd, .theta.2_cmd, .theta.3_cmd respectively corresponding
to the first to third blades 141, 142, and 143 are generated based
on the equation Eq.2. In at least some embodiments, for generating
the first to third pitch angle reference commands .theta.1_cmd,
.theta.2_cmd, .theta.3_cmd, the control block 40 further includes a
first subtraction element 44, a second subtraction element 45, and
a third subtraction element 46. The first subtraction element 44
subtracts a first reference (mean) angle of attack .alpha.1_ref
from the first mean inflow angle .phi.1 and provides the first
pitch angle reference command .theta.1_cmd representing a
difference between the first mean inflow angle .phi.1 and the first
reference angle of attack .alpha.1_ref. The second subtraction
element 45 subtracts a second reference angle of attack
.alpha.2_ref from the second mean inflow angle .phi.2 and provides
the second pitch angle reference command .theta.2_cmd representing
a difference between the second mean inflow angle .phi.2 and the
second reference angle of attack .alpha.2_ref. The third
subtraction element 46 subtracts a third reference angle of attack
.alpha.3_ref from the third mean inflow angle .phi.3 and provides
the third pitch angle reference command .theta.3_cmd representing a
difference between the third mean inflow angle .phi.3 and the third
reference angle of attack .alpha.3_ref. In this embodiment, the
first mean inflow angle calculation unit 41, the second mean inflow
angle calculation unit 42, the third mean inflow angle calculation
unit 43, the angle of attack calculation unit 48, and the three
subtraction elements 44, 45, 46 together act as a pitch angle
reference command calculation unit used to calculate the first to
third pitch angle reference commands .theta.1_cmd, .theta.2_cmd,
.theta.3_cmd corresponding to the first to third blades 141, 142,
143 respectively.
[0039] In step 57, the controller 26 receives the calculated first
to third pitch angle reference commands .theta.1_cmd, .theta.2_cmd,
.theta.3_cmd, and other reference commands from the scheduler 22
and receives the estimated parameters from the estimator 24 and the
sensed signals from the sensors, and then calculates corresponding
control commands to control the wind turbine 10. Because the pitch
angle reference commands .theta.1_cmd, .theta.2_cmd, .theta.3_cmd
provide reference for mitigating loads during yaw error, the
control commands, such as pitch commands on each of the blades 141,
142, 143 and the torque commands generated by the controller 26 can
mitigate loads during yaw error. After the adjusted control
commands are generated based on the calculated first to third pitch
angle reference commands .theta.1_cmd, .theta.2_cmd, .theta.3_cmd,
the process proceeds back to the step 51, and thus this control
block 40 can provide the pitch angle reference commands
.theta.1_cmd, .theta.2_cmd, .theta.3_cmd during operation of the
wind turbine 10 for mitigating loads during yaw error thereof.
[0040] FIG. 6 is a comparison diagram of a simulation of a trend 62
of pitch angles of three blades when not controlled by the control
method 50 of FIG. 5 and a trend 64 of pitch angles of three blades
when controlled by the control method 50 of FIG. 5. When not
controlled by the control method 50 of FIG. 5, the pitch angles of
three blades are controlled almost simultaneously and to same
adjusting degrees. However, for the control method 50 of FIG. 5,
the pitch angles of three blades are controlled respectively
corresponding individual first to third blades. Namely, the control
method 50 respectively controls the pitch angles of the three
blades based on the yaw error respectively affected on each
individual blade, which can reduce imbalance load on the three
blades and then improve effect on mitigating loads.
[0041] FIG. 7 is a comparison diagram of a simulation of a trend 72
of a resultant load of a wind turbine not controlled by the control
method 50 of FIG. 5 and a trend 74 of a resultant load of a wind
turbine controlled by the control method 50 of FIG. 5 while
maintaining the rotor speed the same as in the conventional control
method. The trend 72 of the resultant load when not controlled by
the control method 50 of FIG. 5 is greater than the trend 74 of the
resultant load under the control method 50 of the present
disclosure. Thus the control method 50 is viewed as being an
improvement, due to the control method 50 controlling the pitch
angles of the three blades 141,142, and 143 respectively while not
controlling the pitch angles of the three blades 141, 142, and 143
to the same degree.
[0042] In other embodiments, the control method 50 may combine
other control methods together to reduce the influence of the yaw
error, for example combine a speed control method to modify the
related speeds such as rotor speed, generator speed, and the like.
In one embodiment, the rotor speed may be determined by one or more
of the calculated yaw error, the measured wind speed, or other
related parameters. For example, Eq. 1 suggests that maintaining a
higher rotor speed .OMEGA. will result in smaller inflow angle
variations across the three rotor blades 141, 142, 143, leading to
lower asymmetric bending loads on the rotor.
[0043] As an example, FIG. 8 shows a schematic diagram of a control
block 80 of the scheduler 22, for further providing rotor speed and
power setting control combined with the pitch control mentioned
above. The control block 80 includes a rotor speed reference
command setting unit 82 and a power reference command setting unit
84. The rotor speed reference command setting unit 82 is used to
receive the yaw error calculated by the yaw error calculation unit
49 (see FIG. 4), and then estimate/calculate a rotor speed
reference command .OMEGA._cmd based at least on the yaw error or
based on the yaw error and other related parameters. The controller
26 will produce a rotor speed command (not shown) at least
according to the rotor speed reference command .OMEGA._cmd, to
regulate the rotor speed of the wind turbine 10. In one embodiment,
the rotor speed reference command .OMEGA._cmd is predetermined
according to the real yaw error and wind speed through appropriate
algorithms. In one embodiment, the rotor speed reference command
.OMEGA._cmd may only include a high speed mode used for the yaw
error condition, and a normal speed mode used for a normal working
status.
[0044] Similarly, the power speed reference command setting unit 84
is used to receive the yaw error calculated by the yaw error
calculation unit 49 (see FIG. 4), and then estimate/calculate a
power reference command P_cmd based at least on the yaw error or
based on the yaw error and other related parameters. The controller
26 will produce power command (not shown) at least according to the
power reference command P_cmd, to regulate the power of the wind
turbine 10. In one embodiment, the power reference command P_cmd is
predetermined according to the real yaw error, wind speed, wind
direction, load measurement, etc., through appropriate algorithms.
In other embodiments, other control parameters such as torque may
be also calculated based on the yaw error, which is used to
generate corresponding control commands (like the pitch commands)
of the controller 26, to further mitigating loads during yaw
error.
[0045] Referring to FIG. 9, a schematic diagram of a control block
90 of the scheduler 22, for mitigating loads during yaw error on
the wind turbine 10 is shown, according to another embodiment. Like
the control block 40 of FIG. 4, this control block 90 is also used
to provide three pitch angle reference commands (.theta.1_cmd,
.theta.2_cmd, .theta.3_cmd) to the controller 26 for every blade
141, 142, 143, but designed as a different configuration. In this
illustrated embodiment of FIG. 9, the control block 90 includes a
first mean AoA calculation unit 911, a second mean AoA calculation
unit 912, a third mean AoA calculation unit 913, three subtraction
elements 914, 915, and 916, an AoA limit unit 917, three block
elements 918, 919, 920, and three summation elements 921, 922, and
923.
[0046] The first mean AoA calculation unit 911 is used to calculate
an angle of attack AoA1 corresponding to the first blade 141, based
on a pitch angle feedback signals .theta.1_fbk, and the parameter
signals V1, .beta.1, .lamda.1, .OMEGA. mentioned above according to
the equations Eq. 1 and Eq. 2. Similarly, the second mean AoA
calculation unit 912 is used to calculate an angle of attack AoA2
corresponding to the second blade 141, based on a pitch angle
feedback signals .theta.2_fbk, and the parameter signals V2,
.beta.2, .lamda.2, .OMEGA. mentioned above according to the
equations Eq. 1 and Eq. 2. The third mean AoA calculation unit 913
is used to calculate an angle of attack AoA3 corresponding to the
third blade 143, based on a pitch angle feedback signals
.theta.3_fbk, and the parameter signals V3, .beta.3, .lamda.3,
.OMEGA. mentioned above according to the equations Eq. 1 and Eq. 2.
The first to third wind speeds V1, V2, V3 may be equal, the first
to third wind directions .beta.1, .beta.2, and .beta.3 may be equal
in some embodiments.
[0047] The AoA limit unit 917 is used to set an AoA limitation
value (or a range) for limiting the AoA of every blade under a
predetermined maximum limitation value AoA_lim based on the yaw
error calculated by the yaw error calculation unit 49 (see FIG. 4),
or based on a predetermined yaw error condition. The predetermined
maximum limitation value AoA_lim is prestored in the AoA limit unit
917 in advance, and it can be changed according to different
conditions, for example if the wind turbine 10 is changed, the
predetermined maximum limitation value AoA_lim may be changed
accordingly.
[0048] The subtraction element 914 is used to subtract the angle of
attack AoA1 from the predetermined maximum limitation value AoA_lim
and provides a first AoA error .DELTA.AoA1 representing a
difference between the angle of attack AoA1 and the limitation
value AoA_lim. Similarly, the subtraction element 915 is used to
subtract the angle of attack AoA2 from the predetermined maximum
limitation value AoA_lim and provides a second AoA error
.DELTA.AoA2 representing a difference between the angle of attack
AoA2 and the limitation value AoA_lim The subtraction element 916
is used to subtract the angle of attack AoA3 from the predetermined
maximum limitation value AoA_lim and provides a third AoA error
.DELTA.AoA3 representing a difference between the angle of attack
AoA3 and the limitation value AoA_lim.
[0049] The block element 918 is used to determine whether the first
AoA error .DELTA.AoA1 is greater than zero, and, if so, allow the
first AoA error .DELTA.AoA1 to pass through itself to subsequent
elements, or, if not, block the first AoA error .DELTA.AoA1. In
other words, when the calculated angle of attack AoA1 is greater
than the limitation value AoA_lim, there is a need to provide the
first pitch angle reference command .theta.1_cmd based on the AoA
errors to the controller 26 as mentioned above. In detail, if the
calculated angle of attack AoA1 is greater than the limitation
value AoA_lim, the first AoA error .DELTA.AoA1 is added into the
pitch angle feedback signals .theta.1_fbk through the summation
element 921 to become the first pitch angle reference command
.theta.1_cmd. Similarly, the second and third pitch angle reference
command .theta.2_cmd, .theta.3_cmd are generated by the block
elements 919, 920 and the summation elements 922, 923. In this
illustrated embodiment of FIG. 9, the control block 90 acts as the
pitch angle reference command calculation unit used to calculate
the first to third pitch angle reference commands .theta.1_cmd,
.theta.2_cmd, .theta.3_cmd corresponding to the first to third
blades 141, 142, 143 respectively. In other embodiments, the pitch
angle reference command calculation unit may be varied based upon
different conditions such as the type of the wind turbine or the
location of the wind turbine, etc.
[0050] Referring to FIG. 10, a partial schematic block diagram of
the control system 20 is shown, in accordance with at least some
embodiments of the present disclosure. Compared with FIG. 2, the
control system 20 further includes an individual blade pitch
control unit 28 for providing further compensation for the pitch
commands P1_cmd, P2_cmd, P3_cmd generated by the controller 26. As
mentioned above, the controller 26 generates the pitch commands
P1_cmd, P2_cmd, P3_cmd based on the calculated pitch angle
reference commands .theta.1_cmd, .theta.2_cmd, .theta.3_cmd, and
other reference commands, such as the rotor speed reference command
.OMEGA._cmd, the power reference command P_cmd, and a selected
control mode reference command, etc. In some embodiments, the pitch
commands P1_cmd, P2_cmd, P3_cmd may be equal, called collective
pitch commands. For example, if the selected control mode reference
command demands power reference tracking, this would typically be
achieved by the controller 26 through the collective pitch commands
(same pitch angle sent to all three blades) and torque commands.
Even through the collective pitch commands P1_cmd, P2_cmd, P3_cmd
can mitigate loads during yaw error on the wind turbine 10, further
reduction may be achieved by introducing the individual blade pitch
control unit 28. In general, the individual blade pitch control
unit 28 is used to generate three pitch angle compensation commands
.DELTA..theta.1, .DELTA..theta.2, .DELTA..theta.3 to respectively
compensate the collective pitch commands P1_cmd, P2_cmd, P3_cmd
corresponding to the three blades 141, 142, and 143, which can
reduce asymmetric bending loads thereon.
[0051] In one embodiment, the control system 20 further includes
three summation elements 21, 23, 25, used to compensate the pitch
commands P1_cmd, P2_cmd, P3_cmd through the pitch angle
compensation commands .DELTA..theta.1, .DELTA..theta.2,
.DELTA..theta.3. In detail, the summation element 21 adds the pitch
command P1_cmd to the pitch angle compensation command
.DELTA..theta.1, and provides a compensated pitch command P1_cmd'
representing a summation of the pitch command P1_cmd and the pitch
angle compensation command .DELTA.A.theta.1. Similarly, the
summation element 23 adds the pitch command P2_cmd to the pitch
angle compensation command .DELTA..theta.2, and provides a
compensated pitch command P2_cmd' representing a summation of the
pitch command P2_cmd and the pitch angle compensation command
.DELTA..theta.2. The summation element 25 adds the pitch command
P3_cmd to the pitch angle compensation command .DELTA..theta.3, and
provides a compensated pitch command P3_cmd' representing a
summation of the pitch command P3_cmd and the pitch angle
compensation command .DELTA..theta.3.
[0052] Referring to FIG. 11, a schematic diagram of the individual
blade pitch control unit 28 is shown, in accordance with one
embodiment of the present disclosure. The individual blade pitch
control unit 28 includes a fourth mean AoA calculation unit 281, a
fifth mean AoA calculation unit 282, a sixth mean AoA calculation
unit 283, an average AoA calculation unit 284, and three
subtraction elements 285, 286, 287. Similar to the embodiment of
FIG. 9, the fourth to sixth mean AoA calculation units 281, 282,
283 have the similar function as the first to third mean AoA
calculation units 911, 912, 913, and are thus not described here
again. Therefore, three angles of attack AoA1, AoA2, AoA3 are
determined accordingly. The first to third wind speeds V1, V2, V3
may be equal, the first to third wind directions .beta.1, .beta.2,
and .beta.3 may be equal in some embodiments.
[0053] The average AoA calculation unit 284 is used to receive the
three angles of attack AoA1, AoA2, AoA3, and then calculate an
average AoA value AoA_avg by adding three angles of attack AoA1,
AoA2, AoA3 and divided by three. The subtraction element 285
subtracts the average AoA value AoA_avg from the angle of attack
AoA1 and provides the pitch angle compensation command 401
representing a difference between the average AoA value AoA_avg and
the angle of attack AoA1. Similarly, the subtraction element 286
subtracts the average AoA value AoA_avg from the angle of attack
AoA2 and provides the pitch angle compensation command
.DELTA..theta.2 representing a difference between the average AoA
value AoA_avg and the angle of attack AoA2. The subtraction element
287 subtracts the average AoA value AoA_avg from the angle of
attack AoA3 and provides the pitch angle compensation command
.DELTA..theta.3 representing a difference between the average AoA
value AoA_avg and the angle of attack AoA3. Referring back to FIG.
10, due to the pitch commands P1_cmd, P2_cmd, P3_cmd being
compensated by the pitch angle compensation commands
.DELTA..theta.1, .DELTA..theta.2, .DELTA..theta.3, the compensated
pitch commands P1_cmd', P2_cmd', P3_cmd' can further mitigate loads
during yaw error on the wind turbine 10 based on the compensation
of the pitch angle reference commands (.theta.1_cmd, .theta.2_cmd,
.theta.3_cmd) and, for example, further avoid flow separation on
the three blades 141, 142, 143.
[0054] FIG. 12 shows a schematic diagram of the individual blade
pitch control unit 28, in accordance with another embodiment of the
present disclosure. Compared with the embodiment of FIG. 11, this
embodiment uses a fourth mean inflow angle calculation unit 288, a
fifth mean inflow angle calculation unit 289, and a sixth mean
inflow angle calculation unit 290, to replace the three units 281,
282, 283 of FIG. 11 and to produce three mean inflow angles .phi.1,
.phi.2, .phi.3. The calculation method of the three mean inflow
angles .phi.1, .phi.2, and .phi.3 has been described in FIG. 4 and
is thus not described here again. Accordingly, an average inflow
angle calculation unit 291 is introduced to calculate an average
value .phi._avg like the average AoA calculation unit 284 of FIG.
11. And three subtraction elements 292, 293, 294 are further
introduced to produce three pitch angle compensation commands
.DELTA..theta.1, .DELTA..theta.2, .DELTA..theta.3 with similar mode
of the embodiments of FIG. 11. In other embodiments, the
configuration of the individual blade pitch control unit 28 can be
adjusted according to other appropriate compensation algorithms.
The first to third wind speeds V1, V2, V3 may be equal, the first
to third wind directions .beta.1, .beta.2, and .beta.3 may be equal
in some other embodiments.
[0055] While the invention has been described with reference to
exemplary embodiments, it will be understood by those skilled in
the art that various changes may be made and equivalents may be
substituted for elements thereof without departing from the scope
of the invention. In addition, many modifications may be made to
adapt a particular situation or material to the teachings of the
invention without departing from the essential scope thereof.
Therefore, it is intended that the invention not be limited to the
particular embodiment disclosed as the best mode contemplated for
carrying out this invention, but that the invention will include
all embodiments falling within the scope of the appended
claims.
* * * * *